Xiao Ming installed $$$n$$$ lights in his new home but forgot to install switches. So he hired $$$m$$$ electricians to install switches for him. These $$$m$$$ electricians are all novices who came to practice switch installation at Xiao Ming's home, so they don't charge for their work.

The electricians arrive and work one by one. When the $$$i$$$-th electrician arrives, he brings a switch and selects $$$k$$$ lights $$$a_1,a_2,...,a_k$$$ from the $$$n$$$ lights to connect them together. Each time this switch is pressed, every one of these $$$k$$$ lights will toggle its state (on becomes off, off becomes on).

Since these novice electricians are here to practice, the set of lights they connect must satisfy the following condition: $$$\mathbf{At\ least\ one\ of\ the \ lights\ connected \ by\ their\ switch\ was \ previously\ connected\ by}$$$$$$\mathbf{\ at\ most\ one\ switch\ before\ theirs.}$$$

After living there for several years, Xiao Ming suddenly discovered that all the switches in his home had broken, but some lights were still on. Due to the passage of time, Xiao Ming could no longer remember the original installation order of the switches, $$$\mathbf{and\ all\ switches\ have\ been\ renumbered}$$$. Now these novice electricians have all become senior electricians, and repairing the $$$i$$$-th switch costs $$$c_i$$$ yuan.

Xiao Ming wants to know the minimum amount of money needed to repair the switches so that he can now turn off all the lights.